Where are the branches in a many-body wavefunction?
Jess Riedel, Perimeter Institute
When the wavefunction of a macroscopic system (such as the universe) unitarily evolves from a low-entropy initial state, we expect that it develops quasiclassical "branches", i.e., a decomposition into orthogonal components each taking well-defined, distinct values for macroscopic observables. Is this decomposition unique? Can the number of branches decrease in time? Answering these questions is hard because branches are defined only intuitively, much like early investigations of algorithms prior to the Church–Turing thesis.
A rigorous definition would give an exponential speed up to certain non-stationary matrix-product state numerical simulations, as well as solve Kent's Set Selection problem in the consistent histories formalism, a 20-year-old open challenge in the foundations of quantum mechanics. I introduce some tentative definitions based on the idea of redundant information and the phenomenon of quantum Darwinism, and establishing several related uniqueness theorems. A key counterexample is provided by the Shor error-correction code, which demonstrates that branch structure with robust, redundant records on macroscopic scales can hide incompatible (noncommuting) structure on microscopic scales, with speculative implications to holographic situations where locality breaks down.